Nonlinear Price Impact and Portfolio Choice

31 Pages Posted: 2 Jun 2015 Last revised: 16 May 2018

See all articles by Paolo Guasoni

Paolo Guasoni

Dublin City University - School of Mathematical Sciences; Boston University - Department of Mathematics and Statistics

Marko Weber

National University of Singapore (NUS) - Department of Mathematics

Date Written: June 2, 2015

Abstract

In a market with price-impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long-term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the curvature of the price-impact function. Trading rates are finite as with linear impact, but are lower near the target portfolio, and higher away from the target. The model nests the square-root impact law and, as extreme cases, linear impact and proportional transaction costs.

Keywords: price-impact, square-root law, trading volume

JEL Classification: G11, G12

Suggested Citation

Guasoni, Paolo and Weber, Marko, Nonlinear Price Impact and Portfolio Choice (June 2, 2015). Available at SSRN: https://ssrn.com/abstract=2613284 or http://dx.doi.org/10.2139/ssrn.2613284

Paolo Guasoni (Contact Author)

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

HOME PAGE: http://www.guasoni.com

Boston University - Department of Mathematics and Statistics ( email )

Boston, MA 02215
United States

Marko Weber

National University of Singapore (NUS) - Department of Mathematics ( email )

Department of Mathematics
Singapore, 117543
Singapore

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